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Publication Nash Equilibria in certain two-choice multi-player games played on the ladder graph(World Scientific Publishing, 2021-01-16) Sánchez Muñoz, Victoria; Mc Gettrick, MichaelIn this paper, we compute analytically the number of Nash Equilibria (NE) for a two-choice game played on a (circular) ladder graph with 2n players. We consider a set of games with generic payoff parameters, with the only requirement that a NE occurs if the players choose opposite strategies (anti-coordination game). The results show that for both, the ladder and circular ladder, the number of NE grows exponentially with (half) the number of players n, as NNE(2n)∼C(φ)n, where φ=1.618.. is the golden ratio and Ccirc>Cladder. In addition, the value of the scaling factor Cladder depends on the value of the payoff parameters. However, that is no longer true for the circular ladder (3-degree graph), that is, Ccirc is constant, which might suggest that the topology of the graph indeed plays an important role for setting the number of NE.Publication Computational Selection of Transcriptomics Experiments Improves Guilt-by-Association Analyses(PLos ONE, 2012-08-07) Yang, Haixuan; HY and AP were supported by the United Kingdom Biotechnology and Biological Sciences Research Council (BBSRC) New Investigator Grant BB/F00964X/1 (http://www.bbsrc.ac.uk/). PB was supported by the Agnes Grace Allen Endowment and the School of Biological Sciences at Royal Holloway, University of London (http://www.rhul.ac.uk/home.aspx). AD was supported by the BBSRC New Investigator Grant BB/E003486/1 (http://www.bbsrc.ac.uk/). LB was supported by BBSRC grant FP7-PEOPLE-ITN-2009-PIEF-GA-2009-255035 (http://cordis.europa.eu/fp7/people/home_en.html).The Guilt-by-Association (GBA) principle, according to which genes with similar expression profiles are functionally associated, is widely applied for functional analyses using large heterogeneous collections of transcriptomics data. However, the use of such large collections could hamper GBA functional analysis for genes whose expression is condition specific. In these cases a smaller set of condition related experiments should instead be used, but identifying such functionally relevant experiments from large collections based on literature knowledge alone is an impractical task. We begin this paper by analyzing, both from a mathematical and a biological point of view, why only condition specific experiments should be used in GBA functional analysis. We are able to show that this phenomenon is independent of the functional categorization scheme and of the organisms being analyzed. We then present a semi-supervised algorithm that can select functionally relevant experiments from large collections of transcriptomics experiments. Our algorithm is able to select experiments relevant to a given GO term, MIPS FunCat term or even KEGG pathways. We extensively test our algorithm on large dataset collections for yeast and Arabidopsis. We demonstrate that: using the selected experiments there is a statistically significant improvement in correlation between genes in the functional category of interest; the selected experiments improve GBA-based gene function prediction; the effectiveness of the selected experiments increases with annotation specificity; our algorithm can be successfully applied to GBA-based pathway reconstruction. Importantly, the set of experiments selected by the algorithm reflects the existing literature knowledge about the experiments.Publication Bioassay models with natural mortality and random effects(2011) Hinde, John; Conesa, D, Forte, A., Lopez-Quiles, A. and Munoz, F.; |~|In fitting dose-response models to entomological data it is often necessary to take account of natural mortality and/or overdispersion. The standard approach to handle natural mortality is to use Abbott¿s formula. Standard overdispersion models include beta-binomial models, logistic-normal, and discrete mixtures. Here we consider combining these two aspects with extensions that allow for the modelling of the natural mortality and overdispersion. Two models are developed: one including a random effect in the linear predictor and other including a random effect in the natural mortality. We consider the application of these models to data from an experiment on the use of a virus (PhopGV) for the biological control of worm larvae (Phthorimaea operculella) in potatoes. Using the models with random effects, we obtained a better fit than that provided by the standard model.Publication Analyzing time-course microarray data using functional data analysis - a review(Statistical Applications in Genetics and Molecular Biology, 2011-05) Coffey, Norma; Hinde, John; Science Foundation Ireland under Grant No. 07/MI/012; Science Foundation IrelandGene expression over time can be viewed as a continuous process and therefore represented as a continuous curve or function. Functional data analysis (FDA) is a statistical methodology used to analyze functional data that has become increasingly popular in the analysis of time-course gene expression data. Several FDA techniques have been applied to gene expression profiles including functional regression analysis (to describe the relationship between expression profiles and other covariate(s)), functional discriminant analysis (to discriminate and classify groups of genes) and functional principal components analysis (for dimension reduction and clustering). This paper reviews the use of FDA and it¿s associated methods to analyze time-course microarray gene expression data.